Brownian dynamics simulations of protein folding: Access to milliseconds time scale and beyond

Protein folding occurs on a time scale ranging from milliseconds to minutes for a majority of proteins. Computer simulation of protein folding, from a random configuration to the native structure, is nontrivial owing to the large disparity between the simulation and folding time scales. As an effort to overcome this limitation, simple models with idealized protein subdomains, e.g., the diffusion–collision model of Karplus and Weaver, have gained some popularity. We present here new results for the folding of a four-helix bundle within the framework of the diffusion–collision model. Even with such simplifying assumptions, a direct application of standard Brownian dynamics methods would consume 10,000 processor-years on current supercomputers. We circumvent this difficulty by invoking a special Brownian dynamics simulation. The method features the calculation of the mean passage time of an event from the flux overpopulation method and the sampling of events that lead to productive collisions even if their probability is extremely small (because of large free-energy barriers that separate them from the higher probability events). Using these developments, we demonstrate that a coarse-grained model of the four-helix bundle can be simulated in several days on current supercomputers. Furthermore, such simulations yield folding times that are in the range of time scales observed in experiments.

Adaptive mutations in Escherichia coli as a model for the multiple mutational origins of tumors.

The cells in most tumors are found to carry multiple mutations; however, based upon mutation rates determined by fluctuation tests, the frequency of such multiple mutations should be so low that tumors are never detected within human populations. Fluctuation tests, which determine the cell-division-dependent mutation rate per cell generation in growing cells, may not be appropriate for estimating mutation rates in nondividing or very slowly dividing cells. Recent studies of time-dependent, "adaptive" mutations in nondividing populations of microorganisms suggest that similar measurements may be more appropriate to understanding the mutation origins of tumors. Here I use the ebgR and ebgA genes of Escherichia coli to measure adaptive mutation rates where multiple mutations are required for rapid growth. Mutations in either ebgA or ebgR allow very slow growth on lactulose (4-O-beta-D-galactosyl-D-fructose), with doubling times of 3.2 and 17.3 days, respectively. However, when both mutations are present, cells can grow rapidly with doubling times of 2.7 hr. I show that during prolonged (28-day) selection for growth on lactulose, the number of lactulose-utilizing mutants that accumulate is 40,000 times greater than can be accounted for on the basis of mutation rates measured by fluctuation tests, but is entirely consistent with the time-dependent adaptive mutation rates measured under the same conditions of prolonged selection.